Accelerated Random-Sweep Gibbs Sampling for Gaussian Graphical Models via Dual Normal Factor Graphs

We study the convergence properties of the random-sweep Gibbs sampler for Gaussian graphical models with a thin-membrane prior. We demonstrate that the convergence rate of the Gibbs sampler is significantly accelerated in the dual model, which is obtained by applying the Fourier transform to the local factors of the normal factor graph representing the original model. In both domains, we derive the exact convergence rates for homogeneous $k$-regular graphs. We prove that, for all homogeneous models whose graphical representations contain cycles, the convergence rate in the dual domain is universal and independent of the underlying graph topology. Moreover, we show that the effective convergence rate in the dual domain is governed by the algebraic connectivity of the graph, providing an additional acceleration without increasing the computational complexity per sweep. We further establish an explicit algebraic relation between the covariance structures of the primal and dual models, enabling marginal statistics of the primal model to be recovered directly from those of the dual model. Finally, numerical experiments on several graph families confirm our theoretical results and demonstrate substantial improvements in the convergence rates in various settings.

LORE: Lagrangian-Optimized Robust Embeddings for Visual Encoders

Visual encoders have become fundamental components in modern computer vision pipelines. However, ensuring robustness against adversarial perturbations remains a critical challenge. Recent efforts have explored both supervised and unsupervised adversarial fine-tuning strategies. We identify two key limitations in these approaches: (i) they often suffer from instability, especially during the early stages of fine-tuning, resulting in suboptimal convergence and degraded performance on clean data, and (ii) they exhibit a suboptimal trade-off between robustness and clean data accuracy, hindering the simultaneous optimization of both objectives. To overcome these challenges, we propose Lagrangian-Optimized Robust Embeddings (LORE), a novel unsupervised adversarial fine-tuning framework. LORE utilizes constrained optimization, which offers a principled approach to balancing competing goals, such as improving robustness while preserving nominal performance. By enforcing embedding-space proximity constraints, LORE effectively maintains clean data performance throughout adversarial fine-tuning. Extensive experiments show that LORE significantly improves zero-shot adversarial robustness with minimal degradation in clean data accuracy. Furthermore, we demonstrate the effectiveness of the adversarially fine-tuned CLIP image encoder in out-of-distribution generalization and enhancing the interpretability of image embeddings.

Aligning Visual Contrastive learning models via Preference Optimization

Contrastive learning models have demonstrated impressive abilities to capture semantic similarities by aligning representations in the embedding space. However, their performance can be limited by the quality of the training data and its inherent biases. While Reinforcement Learning from Human Feedback (RLHF) and Direct Preference Optimization (DPO) have been applied to generative models to align them with human preferences, their use in contrastive learning has yet to be explored. This paper introduces a novel method for training contrastive learning models using Preference Optimization (PO) to break down complex concepts. Our method systematically aligns model behavior with desired preferences, enhancing performance on the targeted task. In particular, we focus on enhancing model robustness against typographic attacks, commonly seen in contrastive models like CLIP. We further apply our method to disentangle gender understanding and mitigate gender biases, offering a more nuanced control over these sensitive attributes. Our experiments demonstrate that models trained using PO outperform standard contrastive learning techniques while retaining their ability to handle adversarial challenges and maintain accuracy on other downstream tasks. This makes our method well-suited for tasks requiring fairness, robustness, and alignment with specific preferences. We evaluate our method on several vision-language tasks, tackling challenges such as typographic attacks. Additionally, we explore the model's ability to disentangle gender concepts and mitigate gender bias, showcasing the versatility of our approach.